Quantum Circuits as a Dynamical Resource to Learn Nonequilibrium Long-Range Order

TL;DR

This paper demonstrates that quantum circuits can generate and learn long-range ordered states in nonequilibrium conditions, surpassing equilibrium limitations and enabling new quantum phases with enhanced properties.

Contribution

It introduces variational quantum circuits capable of creating long-range ordered states at finite energy density, expanding the scope of quantum phase engineering beyond equilibrium constraints.

Findings

Quantum circuits can produce symmetry-broken states with long-range order.

Learned states exhibit high quantum Fisher information, similar to GHZ states.

These states are robust against local measurements, indicating potential for quantum metrology.

Abstract

Equilibrium statistical ensembles impose stringent constraints on phases of quantum matter. For example, the Mermin-Wagner theorem prohibits long-range order in low-dimensional systems beyond the ground state. Here, we show that quantum circuits can learn states of matter with long-range order that are inaccessible in equilibrium. We construct variational quantum circuits that generate symmetry-broken and symmetry-protected topological states with long-range order in one-dimensional systems at finite energy density, where equilibrium states are typically featureless. Importantly, the learned states can exhibit unconventional features with enhanced metrological properties such as a quantum Fisher information close to a GHZ state, but robust against local measurements. Our work establishes coherent quantum dynamics as a powerful resource for engineering nonequilibrium phases of matter, opening a path toward a broader dynamical scope of quantum order beyond the constraints of equilibrium ensembles.